Win Myat Aye, Myanmar's social welfare minister, made the comments in Dhaka late Thursday after visiting one of the Bangladesh camps struggling to provide for some of the one million Rohingya Muslims who have fled the country.
A Rohingya community leader confirmed the family's return.
The stateless Muslim minority has been massing in squalid refugee camps across the border in Bangladesh since the Myanmar army launched a ruthless campaign against the community in northern Rakhine state last August.
Doctors Without Borders says the violence claimed at least 6,700 Rohingya lives in the first month alone.
The two countries agreed in December to begin repatriating them in January, but they were delayed by concerns among aid workers and Rohingya that they would be forced to return and face unsafe conditions in Myanmar.
A Facebook post on the official page of Myanmar's Information Committee appears to show the family getting health checks and receiving packages of rice, mosquito netting, and blankets. "The five members of a family ... came back to Taungpyoletwei town repatriation camp in Rakhine state". Myanmar authorities have since bulldozed numerous burned villages, raising alarm from rights groups who say they are erasing evidence of atrocities and obscuring the Rohingya's ties to the country.
The Facebook post does not mention further plans to repatriate more Rohingya. However, Bangladesh and the United Nations refugee agency disputed the repatriation claim.
Although the Rohingya have lived in Myanmar for many generations, most people in Myanmar consider them unwanted immigrants from neighboring Bangladesh and refer to them as "Bengalis, " a term the Rohingya consider derogatory.
"Right now, the conditions are not conducive to a voluntary, dignified and sustainable return", Ursula Mueller, assistant secretary general for the UN's Office for the Coordination of Humanitarian Affairs, told AFP earlier this month after a visit to Rakhine.
Officials said several issues remained unresolved with Myanmar and pointed out that the transit camps in Myanmar where refugees will stay were not yet ready.
Rahim said they demanded to be recognized as citizens of Myanmar before the repatriation starts and that their security arrangements be supervised by the United Nations. "Only sustained global engagement can ensure the rights of the Rohingyas so that they could return to their homes and live there with peace and dignity".
Meanwhile, boats carrying Rohingya from Rakhine state continue to leave Myanmar.
"I hope, Myanmar will repatriate all the families within the possible shortest time", the home minister said.
More than 670,000 Rohingya fled violence in Myanmar since last August, joining an estimated 200,000 Rohingya who have sought shelter in Bangladesh, arriving in waves over the past decades.
"We also appreciate Indian government's initiative for rehabilitation projects in Myanmar for constructing prefabricated houses along with China and Japan, for the Rohingyas", he added.
The agency also noted that in the absence of a UNHCR-Myanmar-Bangladesh agreement, it has continued to engage with both Governments in negotiations on two separate memoranda of understanding (MOUs), meant to ensure that any future returns are conducted in line with the global standards.
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